Mastering Mathematical Thinking: 4th Class · 4th Class · Data · Summer Term

Exploring Chance and Likelihood

Investigate the language of chance by deciding if events are certain, likely, unlikely, or impossible to happen.

TL;DR:Let's become fortune tellers! This topic helps your pupils explore the future by learning the mathematical language to describe what might happen next.

• NCCA Curriculum Specifications
• NCCA: Primary School Mathematics Curriculum - Data - Chance

About This Topic

This topic introduces pupils in Fourth Class to the foundational concepts of probability, as outlined in the Data strand of the Irish Primary School Mathematics Curriculum. The focus is on developing and using the language of chance rather than on formal numerical probability. Pupils will move from informal, everyday language to more precise mathematical terms like 'certain', 'likely', 'unlikely', and 'impossible'. The learning should be grounded in practical, hands-on activities that encourage discussion and reasoning. By exploring simple events and experiments, such as rolling dice, flipping coins, or drawing items from a bag, pupils learn to analyse situations and make reasoned judgements about the likelihood of different outcomes.

The core of this unit is 'maths talk'. Encouraging pupils to articulate why they believe an event is likely or impossible is crucial for developing their mathematical thinking. This topic provides an excellent opportunity to connect mathematics to real-world scenarios that pupils can easily understand, such as weather forecasts, games, and everyday decision-making. The goal is to build an intuitive understanding of chance that will serve as a strong foundation for more formal probability studies in later years.

Key Questions

1. Explain why it is 'impossible' for a dog to meow.
2. Compare the likelihood of rolling a 6 on a die versus rolling a number less than 5.
3. Justify your choice when placing events like 'it will rain tomorrow' and 'the sun will rise tomorrow' on a likelihood scale.

Learning Objectives

• Use the vocabulary of chance: impossible, unlikely, likely, and certain to describe events.
• Order a set of events from least likely to most likely to occur.
• Justify choices when placing events on a likelihood scale.
• Design and conduct simple experiments to explore chance.
• Recognise that some events are more likely to occur than others.

Key Vocabulary

Chance	How likely it is that an event will happen.
Likely	The event will probably happen; there is a good chance.
Unlikely	The event will probably not happen; there is not a good chance.
Certain	The event will definitely happen.
Impossible	The event will definitely not happen.
Outcome	A possible result of an experiment or event, like rolling a 4 on a die.

Watch Out for These Misconceptions

Common Misconception

Confusing 'unlikely' with 'impossible'.

What to Teach Instead

Explain that 'unlikely' means something probably won't happen but it still could. 'Impossible' means it absolutely cannot happen. For example, it's unlikely to snow in June, but it's impossible for a dog to speak English.

Common Misconception

The 'Gambler's Fallacy': thinking that past random events influence future ones.

What to Teach Instead

Clarify that each roll of a die or flip of a coin is an independent event. If you have rolled three sixes in a row, the chance of rolling another six is still exactly the same as it was for the first roll.

Common Misconception

Believing that all outcomes are equally likely in every situation.

What to Teach Instead

Use the 'Mystery Bag' activity with 8 red and 2 blue cubes to demonstrate this. While there are only two possible outcomes of colour, it is much more likely that you will pull out a red cube because there are more of them.

Active Learning Ideas

Human Barometer

Human Chance Line

Create a large line on the floor with labels: 'Impossible', 'Unlikely', 'Likely', 'Certain'. Give pupils cards with different events written on them (e.g., 'It will rain tomorrow', 'A cow will fly through the window') and have them stand on the point of the line that best represents the event's likelihood.

20 min·Whole Class

Human Barometer

Mystery Bag Predictions

In small groups, give each a feely bag containing a mix of coloured cubes, with one colour being much more numerous (e.g., 8 red, 2 blue). Pupils first predict which colour is more likely to be pulled out, then take turns drawing a cube and recording the result before replacing it.

25 min·Small Groups

Human Barometer

Dice Roll Race

In pairs, pupils choose a number from 1 to 6. They then take turns rolling a die, and the first person whose number is rolled ten times wins. This leads to a discussion about whether each number has an equal chance of being rolled.

15 min·Pairs

Real-World Connections

• Reading a weather forecast to decide if you need to bring a coat to school.
• Playing board games that use dice or spinners.
• Understanding sports commentary about a team's chances of winning a match.
• Making everyday choices, like guessing if you are likely to catch the bus if you leave now.
• Participating in a raffle or tombola at a school fair.

Assessment Ideas

Quick Check

Observe pupils during group activities, listening to their use of chance vocabulary and their reasoning. Use a checklist to note which pupils are using the terms correctly.

Quick Check

Provide a worksheet with a list of scenarios. Pupils must label each one as 'impossible', 'unlikely', 'likely', or 'certain'.

Exit Ticket

Ask pupils to complete an 'exit ticket' sentence: 'Today I learned that...' or 'I am still unsure about...'.

Frequently Asked Questions

If something is 'likely', does that mean it will definitely happen?

Not definitely. 'Likely' just means it has a very good chance of happening, but it's not certain. For example, if the sky is full of dark clouds, it's likely to rain, but it's not a certainty.

What is the difference between chance and luck?

In maths, 'chance' is something we can describe and sometimes measure. 'Luck' is a more personal idea about good or bad things happening to you. A coin has a 1 in 2 chance of landing on heads, which is maths, not luck.

Can we ever be 100% certain about anything?

In maths, yes. For example, it is certain that if you roll a standard die, the number will be less than 7. It's also impossible for the number to be 8. These are mathematical certainties.